Elasticity of Calcium and Calcium-Sodium Amphiboles

Transcription

1 Elasticity of Calcium and Calcium-Sodium Amphiboles J. Michael Brown* brown@ess.washington.edu Fax: Evan H. Abramson evan@ess.washington.edu Earth and Space Sciences University of Washington Seattle, WA *Corresponding author Abstract Measurements of single-crystal elastic moduli under ambient conditions are reported for nine calcium to calcium-sodium amphiboles that lie in the composition range of common crustal constituents. Velocities of body and surface acoustic waves measured by Impulsive Stimulated Light Scattering (ISLS) were inverted to determine the 13 moduli characterizing these monoclinic samples. Moduli show a consistent pattern: C33>C22>C11 and C23>C12>C13 and C44>C55~C66 and for the uniquely monoclinic moduli, C35 >>C46~ C25 > C15 ~0. Most of the compositionally-induced variance of moduli is associated with aluminum and iron content. Seven moduli (C11 C12 C13 C22 C44 C55 C66) increase with increasing aluminum while all diagonal moduli decrease with increasing iron. Three moduli (C11, C13 and C44) increase with increasing sodium and potassium occupancy in A-sites. The uniquely monoclinic moduli (C15 C25 and C35) have no significant compositional dependence. Moduli associated with the a* direction (C11 C12 C13 C55 and C66) are substantially smaller than values associated with structurally and chemically related clinopyroxenes. Other moduli are more similar for both inosilicates. The isotropically averaged adiabatic bulk modulus does not vary with iron content but increases with aluminum content from 85 GPa for tremolite to 99 GPa for pargasite. Increasing iron reduces while increasing aluminum increases the isotropic shear modulus which ranges from 47 GPa for ferro-actinolite to 64 for pargasite. These results exhibit far greater anisotropy and higher velocities than apparent in earlier work. Compressional velocities are as fast as ~9 km/s and (intermediate between the a*- and c-axes) are as slow as ~6 km/s. Voigt-Reuss-Hill averaging based on prior single crystal moduli resulted in calculated rock velocities lower than laboratory measurements, leading to adoption of the (higher velocity) Voigt bound. Thus, former uses of the upper Voigt bound can be understood as an ad hoc decision to compensate for inaccurate data. Furthermore, because properties of the endmember amphiboles deviate substantially from prior estimates, all predictions of rock velocities as a function of modal mineralogy and elemental partitioning require reconsideration. Key Words: elasticity, anisotropy, seismic velocities, aggregate elasticity, amphibole, hornblende

2 Introduction Amphiboles are abundant in crustal igneous and metamorphic rocks. They exhibit a wide range of compositions as a result of extensive solid solution behavior, accommodating all of the abundant cation species (silicon, aluminum, magnesium, iron, calcium, sodium, and potassium). The structure also contains ~2 wt% bound water. When subducted, dehydration reactions in rocks containing amphiboles release water at depth that probably affects the evolution of magma in arc volcanism and is likely associated with intermediate and deep earthquakes (Hacker et al. 2003b) as well as seismic tremor/slow slip (Audet et al., 2010). Since amphiboles are ubiquitous, the description of the crustal seismic structure requires characterization of their elastic properties (e.g. Christensen and Mooney 1995, Christensen 1996, Hacker et al. 2003a, Barberini et al. 2007, Tatham et al. 2008, Llana-Funez and Brown 2012, Ji et al. 2013, Selway et al. 2015). However, knowledge concerning their single-crystal elasticity and compositional dependences has remained elusive. In the pioneering work that continues to be cited, Aleksandrov and Ryzhova (1961a) reported single crystal elastic moduli for two hornblendes of unspecified composition based on only slightly over-determined sets of ultrasonic velocity measurements on megacrysts under ambient conditions. As previously demonstrated in studies of feldspars (Brown et al. 2006; Brown et al. 2016; and Waeselmann et al. 2016), results from these early studies have proven to be systematically in error. That the early ultrasonic results under-estimate velocities most likely was a result of open cleavage surfaces and cracks. Also contributing was an inadequate sampling of velocities as a function of propagation direction. Based on the lack of reported chemistry and probable systematic errors, these early results are considered here in the context of having incorrectly influenced various interpretations of crustal seismic structure that were grounded on mineral properties. In particular, in order to better match laboratory measurements, the compensating use of the upper Voigt bound when calculating aggregate rock velocities has been common. In contrast, Watt and O Connell (1980) demonstrated that, in well-characterized and nearly crack-free samples, velocities in two phase aggregates fell within the Hashin- Shtrikman bounds which lie between the extremal Voigt and Reuss bounds (see also Watt et al. 1976). A few determinations of single-crystal elastic properties are available within the broad range of amphibole compositions. Bezacier et al. (2010) gave elastic moduli for a crystal having a composition near the glaucophane end-member. High pressure x-ray cell parameter determinations have been reported for tremolite, pargasite, and glaucophane (Comodi et al. 1991) and for synthetic glaucophane (Jenkins et al. 2010). Hacker et al. (2003a) compiled available (isotropically averaged) elasticity data for important rock-forming minerals including amphiboles. They excluded the Aleksandrov and Ryzhova (1961a) moduli as probably being in error and relied on the Christensen (1996) rock velocity measurements to estimate properties of an average crustal hornblende. To constrain properties of other end-member

3 compositions, they used Holland and Powell (1998) plus the Comodi et al. (1991) compression measurements. Although an isothermal bulk modulus can be inferred from pressure-induced strains, the shear modulus, necessary to estimate body wave velocities, cannot be determined solely from the hydrostatic x-ray data. Instead, Hacker et al. (2003a) estimated shear moduli on the basis of the reported bulk moduli and an assumed Poisson s ratio. They noted that this was a remaining source of uncertainty. As shown later in section 6.3, an isothermal bulk modulus measured under hydrostatic compression (which is equivalent to the elastic aggregate lower-bound Reuss average) is significantly smaller than the appropriate Voigt-Reuss-Hill or Hashin-Shtrikman bulk modulus used for calculation of seismic velocities. Bulk moduli for some amphiboles given by Hacker et al. (2003a) appear to represent the Reuss bound. They combined lower bound moduli (in some cases) in an upperbound Voigt average for calculations of velocities in rocks as mixtures of minerals. Thus, the accuracy of their analysis relied on how well the two errors off-set each other. Here elastic moduli are reported for nine amphiboles that lie in the range of compositions commonly found in crustal rocks (Schumacher 2007). Elastic wave velocities (body wave and surface wave) were measured using Impulsive Stimulated Light Scattering (ISLS) (Abramson et al. 1999). A joint inversion allowed accurate determination of the 13 elastic moduli for these monoclinic minerals. The dependences of moduli on composition are determined through linear regression. From these, relationships to crystal structure and seismic velocities can be explored. Ultimately, more accurate predictions of seismic properties of rocks can be undertaken on the basis of modal mineralogy and elemental partitioning. 2. Amphibole chemistry and structure As reviewed by Hawthorn and Oberti (2007), the monoclinic (C2/m) calcium (including common hornblende) to calcium-sodium amphiboles have a generalized formula of A0-1B2C5T8O22 (OH)2 where the A-site is occupied by sodium and potassium or remains vacant and the B- site is occupied by sodium or calcium. The octahedrally coordinated C-sites contain iron (divalent or trivalent), magnesium, or aluminum (designated as vi Al). The tetrahedral T-sites contain silicon and aluminum (typically up to two aluminum per eight sites, occasionally more, and designated as iv Al). Other common minor chemical components (Ti, Mn, Co, Cr) are found in size and valence-state appropriate sites. Fluorine and chlorine can substitute for OH -1. Figure 1 The naming conventions associated with chemistry of calcium and sodium amphiboles (Hawthorne et al. 2012, see also Leake et al. 1997) are illustrated in Figure 1 using three compositional variables. Aluminum in the T-sites increases from left to right. The site occupancy of A (sodium+potassium) extends in the vertical direction. The solid-solution substitution of sodium for calcium in the B- sites extends into the figure. Although complete solid-solution substitution is

4 possible within this compositional space, several of the stoichiometric compositions are given discrete names. Tremolite is []Ca2Mg5Si8O22(OH)2 (where the brackets denote the vacant A-site) while winchite has one calcium and one sodium in the B- site. Glaucophane has all sodium in the B-site with coupled substitutions of a trivalent cation in C-sites required to balance charge. Hornblende is both an endmember in Figure 1 and is a generalized term for calcium amphiboles with intermediate tetrahedral aluminum compositions. In addition, solid-solution substitution of iron for magnesium gives rise to iron end-members for all phases shown in Figure 1 with ferro- added to the name (e.g. ferro-pargasite). Amphiboles have I-beam structures of two double tetrahedral chains that are bonded to each other by an octahedral sheet with five C-site cations. The I-beams are oriented along the c-axis with A-site cations (when present) bonding the I- beams along the a-axis and B-site cations serving to bond I-beams along the b- direction. Clinopyroxenes share similar chemical variations in a structure that is closely related to the amphiboles, both being inosilicates but the pyroxenes have a single tetrahedral chains aligned along the c-axis. The general formula of the clinopyroxene is BCT2O6 with the B and C sites being equivalent to those found in the amphiboles. End member pyroxenes include diopside (CaMgSi2O6) hedenbergite (CaFeSi2O6), and jadeite (NaAlSi2O6). Having a wide range of solid-solution substitutions for essentially the same crystal structure, amphiboles provide a natural laboratory for the exploration of chemical controls on elasticity. Variations in elastic moduli are anticipated from changes of ionic sizes and charges, as a result of cation substitutions in the A, B, C and T sites. Comparisons of elasticity between pyroxenes and amphiboles provides further opportunities to explore factors influencing elastic behavior. 3. Sample sources and characterization The sources, localities (when known), x-ray determined volumes, and densities of nine amphiboles are given in Table 1. Their structural formula, based on Probe- AMPH (Tindle and Webb, 1994), are given in Table 2 and are plotted in perspective in Figure 1. The underlying microprobe measurements are reported in Table S1 of the supporting materials. Samples 1 and 2 with ~1 sodium in the B-site are classified as calcium-sodium amphiboles. The remaining seven samples are calcium amphiboles. The chemistry of the glaucophane sample used by Bezacier et al. (2010) and the average calcium amphibole composition reported by Schumacher (2007) are also included in Table 2. As noted by Schumacher (2007), calcium amphiboles cover a wide range of intermediate compositions within the compositional space defined in Figure 1 and his reported average (based on over 1700 published analyses) may be a biased estimator of an average hornblende in crustal rocks since samples were analyzed for specific science interests rather than being chosen to best represent crustal chemistry. Nonetheless, this average provides a reference point, defining a common hornblende composition in the following discussion. In Figure 2, sample compositions are projected onto pairs of compositional variables. The nine samples used in this study show a range of compositions that generally brackets the averages reported by Schumacher (2007). This is Table 1 Table 2 Figure 2

5 prerequisite to determining compositional contributions to the elastic properties within the appropriate bounds of elemental partitioning in crustal calcium amphiboles. The following convention is adopted to align the crystallographic axes with respect to the Cartesian axes for the description of the elastic tensor. The Y axis is aligned parallel to the crystallographic b-axis and the Z axis is aligned parallel to the c-axis. The X axis is set in the a*-direction (perpendicular to the b- and c-axes). Elastic moduli (stiffnesses) are represented by the 6 by 6 matrix Cij using the Voigt convention. The inverse of this matrix is the compliance matrix Sij. The vertical sum of the first three rows of the compliance matrix gives six strains, i, associated with the application of unit hydrostatic stress. Based on 2/m symmetry 4 and 6 are zero. These strains can be cast as a 3x3 symmetric tensor which gives crystal compressibility under hydrostatic stress at the limit of zero stress. 4. Experimental methods Both body wave (compressional and transverse) and surface acoustic wave (SAW) velocities were measured using the method of Impulsive Stimulated Light Scattering (ISLS) (Abramson et al. 1999). All measurements (typically between 100 and 200 individual velocity determinations per sample) are reported in Table S2 of the supplementary materials. Details of the experiments and the methods used to determine elastic parameters for low symmetry minerals have been described for body wave measurements (Collins and Brown 1998) and, separately, for SAW measurements (Brown et al. 2006). New in this work is the joint inversion of both body and SAW velocities as described in Brown (2016). Although a complete body wave data set is sufficient to determine all elastic moduli, it proved difficult to obtain a full set of velocities (compressional and two polarizations of transverse waves) for all propagation directions in these natural samples. In some directions, internal flaws scattered light so strongly that the body wave signal could not be recovered from the background and velocities for both polarizations of transverse waves could not be obtained in an adequate number of propagation directions. SAW velocities, based on light coherently scattered from a polished surface, could be more readily measured for all directions of propagation. The typical rms misfit (reported in Table S2) obtained through joint fitting of all measurements is ~0.2%. This is about 12 m/s for SAW and m/s for body waves. Such misfits are essentially identical to those previously reported for individually analyzed body wave and SAW mineral data sets (e.g. Collins and Brown 1998 and Brown et al. 2016) and are representative of intrinsic errors associated with the technique (e.g. Abramson et al. 1999). Thus, no additional systematic errors appear to have been introduced through joint analysis of body wave and SAW velocity determinations. The resulting elastic moduli Cij and their associated 2σ uncertainties are listed in Table 3 for the nine amphiboles plus glaucophane. The compliance matrix elements Sij (inverse of the matrix Cij) and compliances sums, i, are listed in Table S2. The Table 3

6 sums are also given in principal axis coordinates of the hydrostatic compressibility ellipsoid. Body wave velocities for glaucophane in Bezacier et al. (2010) were reanalyzed using the same numerical optimization methods used here. The velocity misfit was reduced from the previously reported 44 m/s (about 0.5%) to 37 m/s. Some of the new moduli differ by ~2 GPa and some uncertainties given by Bezacier et al. (2010) are substantially different from those reported here (see further discussion in Brown 2016). In particular, it would appear that previously reported uncertainties of some off-diagonal moduli were under-estimated and several diagonal uncertainties were over-estimated. Moduli uncertainties for glaucophane are roughly twice as large as those for the calcium and calcium-sodium amphiboles as is appropriate for the observed larger misfit to measured velocities. 5. Elastic moduli and their compositional dependence Elastic moduli and isotropic body wave velocities are plotted in panels of Figure 3 as a function of total aluminum. Also plotted in the panels are predictions based on fits in chemical composition that are described below. The moduli that are non-zero for orthorhombic crystals are shown in the top three panels. The uniquely monoclinic moduli are plotted in the lower left panel. Adiabatic bulk and shear moduli given as the mean of Hashin-Shtrikman bounds (Brown 2015) are shown in the middle lower panel and the resulting isotropic compressional and transverse wave velocities are in the lower right panel. For all compositions the relative sizes of the moduli remain consistent. That is C33>C22>C11 and C23>C12>C13, and C44>C55~C66 and for the uniquely monoclinic moduli, C35 >>C46~ C25 > C15 ~0. The same pattern and roughly similar moduli are apparent for glaucophane. However, the C22, C33, and C23 moduli of glaucophane are significantly stiffer. As further discussed below, the large value of C35 (comparable to the off-diagonal orthorhombic moduli and larger than all other monoclinic moduli) is responsible for a rotation of elastic extrema in the crystallographic plane containing the a- and c-axes. Six chemical controls on elasticity associated with changes in cation charges and sizes can be identified as likely to produce significant effects. These are (1) total aluminum content, or its separate content in either (2) T-sites or (3) C-sites, (4) iron content in C-sites (mainly replacing magnesium), the (5) degree of A-site occupation, and (6) sodium replacement of calcium in B-sites. Other possibilities that are less likely to have a measureable impact (including replacement of OH -1 with Cl -1 or F -1, or changes in the ferric-ferrous iron ratio) could not be studied on the basis of a limited number of samples. Moduli are assumed to be linear in the six compositional metrics identified above. Tremolite is used as the base composition and changing chemical content is given by the formula unit measures listed in Table 2. A standard statistical measure, the F- test (Rencher 2002), determined the significance of the proposed metrics through stepwise addition and removal of terms using MATLAB function stepwiselm. Only three compositional terms were found to have significant impact at the 95% confidence level; these are total aluminum, A-site occupancy, and iron in the C-site. Figure 3

7 Despite the difference in charge and ionic radius, the substitution of sodium for calcium in the B- site appears to have negligible impact on moduli. In addition, at the 95% confidence level, no tested parameterization could reconcile the glaucophane moduli with the calcium and calcium-sodium amphiboles moduli. This suggests that the elasticity of the fully sodium amphibole does not lie on a continuum of linear solid solution behavior or that the experimental uncertainty is larger than estimated. No regression based on compositional vectors that are linear combination of the compositional metrics, as suggested by Schumacher (2007), adequately fit the data. Regression parameters are given in Tables 4 and 5. Blanks in the tables indicate no significant contributions for particular terms. The first column of values gives the estimate for end-member tremolite. Nominal magnesium hornblende (composition as shown in Figure 1) is modeled by adding one aluminum (one times the second column of values for dm/al). For edenite one unit of the third column (dm/da) is added to the hornblende estimate. Fero-actinolite is calculated as the first column (tremolite) plus five times the fourth column (dm/dfe), replacing 5 Mg with 5 Fe. Average experimental uncertainties for the moduli are in the next to last column and the last column gives the rms misfits of the regressions. For the three moduli showing significant sensitivity to A-site occupancy, an alternative model using only total aluminum and iron metrics, is also listed. Most regression misfits are comparable to experimental uncertainty. However, that the regression misfits tend to be larger than experimental uncertainties argue for additional errors or for an incorrectly parameterized chemical dependence. In particular, (1) errors in the determination of sample compositions may be a factor, (2) errors in the moduli may be under estimated, (3) additional compositional metrics may be necessary, or (4) moduli may vary non-linearly with chemistry as was observed in the plagioclase feldspar series (Brown et al. 2016). The regression predictions for moduli and isotropic velocities are shown in Figure 3. Solid lines give the trends associated with increasing aluminum for an iron-free mineral with no A-site occupation. Dashed lines give the predicted behavior of the ferro-equivalent mineral. For moduli showing dependence on A-site occupancy or iron content, the open symbols show predicted moduli. Predicted moduli lie on the solid lines at the appropriate aluminum content if open symbols are not plotted. All diagonal elastic moduli (and the isotropic average shear modulus) are sensitive to iron; these moduli all decrease with the addition of iron. As seen in Table 4 and in Figure 3, the derivatives of the moduli with respect to iron are similar for all diagonal constants. Seven of thirteen moduli (C11 C22 C13 C12 C44 C55 C66) increase with aluminum content while C46 decreases with aluminum. Five moduli (C33 C23 and the monoclinic moduli C15 C25 and C35) have no significant dependence on aluminum. Both isotropic moduli (bulk modulus and shear modulus) increase with added aluminum. A small number of moduli (C11 C13 and C44) are dependent on A-site occupancy. The alternative models with no A-site dependence in Tables 4 and 5 have significantly greater misfit. Note that large deviations between C13 values in Figure 3 and the solid line are well predicted by variations in A-site occupation. In Table 5, all three metrics are necessary to adequately predict the variations of Table 4 Table 5

8 density and the isotropic transverse wave velocities while aluminum and iron content are sufficient to predict compressional velocities. 6. Discussion 6.1 Compositional and structural controls on elasticity In Table 6 the elastic moduli of several amphibole compositions are compared with chemically related clinopyroxene. Amphibole moduli associated with longitudinal stresses and strains involving the a*-axis (ie. C11 C12 C13 C55 C66) are all significantly smaller by approximately a factor of two than the same clinopyroxene moduli while moduli associated with the b- and c-axes (C22 C33 C23 C44) are notably similar. That (as shown in Table 4) C11 and C13 increase with increasing A-site occupation seems reasonable since cations in the A-site provide additional bonding and thus additional resistance to compression along the a*-direction. However, even with full A-site occupations, these amphibole moduli remain smaller than those for pyroxenes (that lack the A-site). The reversal of sign for the uniquely monoclinic moduli (C15 C25 and most importantly C35) are responsible for a major shift in the orientation of anisotropy between amphiboles and pyroxenes that is further discussed below. With a few exceptions, amphiboles and the compositionally related clinopyroxenes show similar patterns: added aluminum increases some moduli and added iron lowers the diagonal moduli. These trends in amphiboles are further explored through comparison of velocity anisotropy and the hydrostatic-induced strain anisotropy. 6.2 Velocity Anisotropy Compressional and transverse wave velocities are shown in Figure 4 as a function of propagation direction in three orthogonal planes. The orientations of crystallographic axes are shown. Light grey circles indicate velocities of 2, 4, 6, 8 and 9.5 km/s. Dark curves give the velocities for the three elastic waves in each plane. For comparison with the amphiboles, the velocities for a nearly iron-free diopside based on moduli reported by Isaak et al. (2006) are shown in the top row; the diopside moduli more recently reported by Sang et al. (2011) are in agreement with the Isaak et al. results. Below that, velocities for the end member amphibole tremolite based on the current study are shown. Compressional velocities based on the elastic moduli of sample I of Aleksandrov and Ryzhova are also plotted along with tremolite. In the third row velocities for pargasite (NaCa2(Mg4Al)(Si6Al2)O22(OH)2) based on the current work are shown. The bottom row gives glaucophane velocities based on measurements of Bezacier et al. (2010). Compressional velocities for both diopside and the amphiboles are uniformly most anisotropic in the X-Z plane (containing the a- and c-axes) and are most isotropic in the Y-Z plane (containing the b- and c-axes). Although not fully symmetric, compressional velocities in the X-Z plane are roughly ellipsoidal (although diopside maintains higher velocities over a broader range of directions) with the semi-major axis rotated from alignment with the c-axis. The diopside semi-major axis is rotated clockwise (associated with positive values for the uniquely monoclinic moduli C15 and C35) while the semi-major axis for all amphiboles is rotated counterclockwise (associated with negative values for C15 and C35). Table 6 Figure 4

9 The maximum compressional velocity for both the diopside and the iron-free amphiboles is >9 km/s. All amphiboles are more anisotropic than clinopyroxenes as a result of the small values of moduli associated with the a* direction (C11 C12 C13 C55 and C66). The lowest compressional velocity for tremolite is ~6 km/s in a direction ~20 counter-clockwise from the positive a*. Pargasite (with more aluminum and full occupancy of the A-site) has a larger minimum velocity of ~7 km/s in roughly the same orientation. Glaucophane compressional velocity anisotropy is intermediate between tremolite and pargasite with the semi-major axis located closer to the c-axis. Based on the compositional derivatives in Table 4, velocities for iron-rich amphiboles (ie. ferro-actinolite and ferro-pargasite) are substantially lower (8.4 km/s in the fast direction and 5.3 km/s in the slowest direction) as a result of smaller values for the diagonal moduli and larger densities. The greater transverse wave anisotropy for amphiboles than for clinopyroxene is evident in Figure 4. Amphibole transverse wave anisotropy ranges from a minimum velocity for tremolite of 3.7 km/s and a maximum of 5.2 km/s. Within the a-b plane transverse velocities for the two transverse wave polarizations are equal in the a*- direction and show the greatest difference in the b-direction. As shown in Figure 4, velocities based on the hornblende moduli reported by Aleksandrov and Ryzhova (1961a) do not compare well with the current amphibole data. Compressional velocities are both significantly smaller and have less anisotropy as shown in the b-c plane. The magnitude of the velocity anisotropy and its orientation relative to crystal axes, as illustrated in the a-c plane, do not match current data. It is likely that these moduli, like the moduli for the feldspars (as previously discussed in Brown et al and Waesselman et al. 2016) are biased as a result of open cleavage surfaces and cracks. The moduli for amphiboles reported here and the previously reported moduli for plagioclase (Brown et al. 2016) and potassium feldspars (Waeselmann et al. 2016), taken together, show that all major crustal mineral phases are highly anisotropic. In fact, they are as anisotropic as the sheet silicates phlogopite (Chheda et al. 2014) and muscovite (Vaughan and Guggenheim 1986). Thus, any preferred orientations of minerals will lead to rocks that exhibit significantly anisotropic velocities. In the absence of alternative data, all past efforts to understand crustal seismic anisotropy and the anisotropy measured in rocks with preferred crystal orientations have relied on the moduli reported by Aleksandrov and Ryzhova (1961a, 1961b). A pragmatic choice, compensating for the low moduli has been to use the Voigt average (upper elastic aggregate bound) rather than the more appropriate Hill or Hashin-Shtrikman average (see also the discussion in Brown et al related to plagioclase minerals). As demonstrated in Figure 4, use of the Aleksandrov and Ryzhova moduli fails to account for the full anisotropy of the amphiboles in rocks containing crystal preferred orientations. It would appear necessary to recalculate properties of amphibole-rich rocks on the basis of more accurate determinations of amphibole elasticity. 393

10 Isotropic moduli and body wave velocities Estimates for the bulk moduli of calcium and sodium amphiboles are summarized in Table 7. In the top row are the results based on the current work plus glaucophane. The Reuss average adiabatic bulk moduli are corrected to isothermal conditions using thermodynamic properties summarized in Hacker et al. (2003a) which results in a reduction by about 1.5%. The values labeled H-S are the mean of the adiabatic Hashin-Shtrikman bounds. Rows labeled C91 (Comodi et al. 1991) and J10 (Jenkins et al. 2010) give isothermal bulk moduli based on x-ray diffraction studies at high pressure. The second value (plus an uncertainty estimate) for the C91 glaucophane, based on a re-analysis by using EoSFit5.2 (Angel 2001), is smaller by over 8%. Jenkins et al. (2010) measured lattice strains in two synthetic glaucophane crystals to 10 GPa and reported an isothermal bulk modulus that lies between the two estimates based on the measurements by Comodi et al. (1991) and is larger than the isotropic average of the elastic moduli of Bezacier et al. (2010). The last row lists the compilation of bulk moduli (Hacker et al. 2003a) used for calculation of compressional and transverse elastic wave velocities in rocks. The range of values given in Table 7 highlight several issues. As apparent in the first row, the large anisotropy of amphiboles leads to large differences between the aggregate bounds. The Reuss-bounded bulk moduli are significantly smaller than the mean of the Hashin-Shtrikman bounds. In addition, the range of glaucophane values based on axes compression measurements indicates that the accuracy of such estimates is highly dependent on the method of analysis and the quality of the data. The compilation of Hacker et al. (2003a) has moduli that appear to over-estimate the dependence on iron and to under-estimate the dependence on aluminum. Some of the Hacker et al. (2003a) entries are more similar to the Reuss bound while other entries are closer to the mean of the upper and lower aggregate bounds. In Table 8 current estimates for the adiabatic shear modulus are compared with the estimates given by Hacker et al. (2003a) that were based on an assumed scaling of Poisson s ratio reported by Christensen (1996). The compilation consistently underestimates the shear modulus for all amphiboles; this would lead to an underprediction of transverse wave velocities. Isotropic body wave velocities for amphiboles are shown in Table 9. The values labeled Literature are based on Hacker et al. (2003a) where two significant figures were given for most elastic moduli. The hornblende in that compilation was based on hornblendite velocities reported by Christensen (1996) to four significant figures. Thus, more precision is provided for the hornblende table entries. The values labeled Current are based on averages of the Hashin-Shtrikman bounds of moduli as a function of composition. The hornblende entry uses the average calcium amphibole composition given by Schumacher (2007). Several trends are clear for the calcium amphiboles. Increasing aluminum leads to higher compressional velocities but this has less impact on transverse wave velocities. Increasing iron decreases both compressional and transverse wave velocities. The estimates of Hacker et al. (2003a) are not consistent with these trends. That the average calcium amphibole has lower density and higher sound speeds than the hornblendite of Christensen (1996) likely reflects a compositional difference Table 7 Table 8 Table 9

11 (assuming more aluminum and more iron moves the prediction in the appropriate direction to better match the hornblendite velocities). Poisson s ratios, σ = 1 [1 2 ((V p ) 2 1 1) ] V s identified by Christensen (1996) as an important discriminator in the interpretation of crustal seismology, are also listed in Table 9. The near constant values for the Literature entries reflect the assumption required in the Hacker et al. (2003a) compilation where no independent determination of the shear modulus was available. In the current work, is shown to be strongly dependent on the iron content of the amphiboles with low values near 0.21 for tremolite, high values of 0.27 for actinolite, and intermediate value of 0.24 for the calcium amphibole average. Increasing aluminum leads to a small positive increase in. The glaucophane of Bezacier et al. has the smallest value for Poisson s ratio. The comparisons made in this section suggest that the predicted isotropic body wave velocities of an average calcium amphibole (hornblende) based on the compositional dependences determined here are in reasonable agreement with laboratory measurements on a hornblendite of unspecified composition. Prior efforts were not able to correctly describe the variation of isotropic elastic wave velocities within the range of amphibole compositions found in crustal rocks. 6.4 Anisotropic strain under hydrostatic stress Projections on two planes of elastic compressibilities under hydrostatic stress, represented using the compliance sums, i, of Table S2 are shown in Figure 5. Three amphiboles (tremolite, pargasite, and glaucophane) and one clinopyroxene (diopside) are plotted. The dashed ellipses are based on the high pressure axis compression analysis of Jenkins et al. (2010) while all other ellipses are calculated from elastic moduli measured under ambient conditions. The panel on the left has strains in the crystallographic a-c plane and the panel on the left has strains in the b- c plane. All amphiboles have the most compliant direction aligned between a*- and c-axes. The semi-major axis of the natural glaucophane (Bezacier et al. 2010) is rotated least from a* and tremolite is rotated most. Although the synthetic glaucophane axes compressions show near isotropic strain in the b-c plane, the elastic moduli measurements of a natural crystal show significant anisotropy that is similar to pargasite. Tremolite in the b-c plane has intermediate anisotropy. The weaker bonding of amphiboles (with vacant or partially filled A- sites) allows greater strain with compression in the general a-axis direction. The structurally and compositionally similar mineral diopside is less compliant in this direction. In the a- c plane, the most and least compressible directions for diopside are rotated by about 90 relative to the amphiboles. The comparisons made in this section indicate that strain under hydrostatic compression calculated on the basis of elastic moduli measured at ambient pressure Figure 5

12 are in general accord with x-ray measurements made at high pressure. However, axes compliances (and the resulting bulk moduli) based on x-ray compression measurements are sensitive to the form of equations of state used to fit the data (e.g. multiple entries are given here in Table 7 and in Jenkins et al. 2010). Such uncertainty can explain the error in the compositional behavior that was previously associated with amphiboles in the compilation by Hacker et al. (2003a) when these measurements provided the only information related to elastic properties of important amphibole end member phases. 7. Summary The full single-crystal elastic moduli of nine natural calcium to calcium-sodium amphiboles have been measured. In addition, velocities of a previously studied natural sodium amphibole have been re-analyzed within the computational framework used in the current study. Clear trends in the behavior of moduli of the calcium and calcium-sodium amphiboles as a function of composition have been identified. A linear fit based on three chemical measures (total aluminum, total iron, and A-site occupation) accounts for most of the compositionally-induced variance in moduli. A linear fit could not reconcile the sodium amphibole glaucophane with the other amphiboles. Either errors in the data or a non-linear dependence on composition are likely. The amphiboles and chemically related clinopyroxenes share similar values of moduli except that amphibole moduli related to the a* direction (C11, C12, C13, C55, and C66) are approximately a factor of two smaller. This is likely associated with the partially occupied or vacant A-site which is associated with bonding in the a-axis direction. Increasing occupation of the A-site increases some of these moduli. In contrast, the substitution of sodium for calcium in the B-site has no significant impact on moduli. The substitution of iron in the C-sites decreases all diagonal elastic moduli while leaving off-diagonal moduli unaffected. The orientation of compressional velocity extrema in the a-c plane is significantly rotated between the amphiboles and the clinopyroxenes. This difference is associated with a large negative value of C35 for amphiboles and a large positive value for clinopyroxenes. The variation of isotropic elastic behavior of amphiboles with composition is important in interpretations of crustal seismology. An earlier compilation (Hacker et al. 2003a), could not, on the basis of then extant data, correctly determine such behavior. Parameters are provided here that allow accurate determination of the isotropic bulk and shear moduli of common amphiboles in crustal rocks. It is noteworthy that amphiboles have higher elastic wave velocities and are more anisotropic than suggested by the early measurements of Aleksandrov and Ryzhova (1961a). In fact, amphiboles exhibit anisotropy nearly as large as that observed in sheet silicates (Aleksandrov and Ryzhova 1961b; Vaughan and Guggenheim 1986; Chheda et al. 2014) and the feldspars (Brown et al. 2006; Brown et al. 2016; and Waeselmann et al. 2016).

13 In efforts to reconcile laboratory measurements on rocks with predictions based on the single-crystal moduli reported by Aleksandrov and Ryzhova (1961a and 1961b), the ad-hoc use of the upper-bound Voigt average is common. This provided partial, but inappropriate, compensation for under-estimated moduli. Furthermore, the earlier moduli fail to account for the full anisotropy of amphiboles. Thus, all predictions of the seismic response of rocks with preferred crystal orientations will need to be re-evaluated. Acknowledgments Support from the National Science Foundation EAR enabled this research. The following students helped prepare samples and collect data: N. Castle, E. Chang, S. Pendleton, K. Pitt, K. Straughan, A. Teel, and H. West-Foyle. The microprobe analyses of S. Kuehner and N. Castle and x-ray analyses of W. Kaminsky were vital contributions to this work. B.W. Evans contributed samples and maintained continuing discussions. The RRUFF database and materials provided by R. Downs are highly appreciated. This research was inspired by a course offered by N. I. Christensen in 1974 on the elasticity of minerals and seismic structure of the crust. It was co-attended by M. Salisbury, D. Fountain, and R. L. Carlson. The science contributions and continued enthusiasm of these colleagues is gratefully acknowledged.

14 References Abramson, E. H., Brown, J. M., and Slutsky, L. J. (1999) Applications of impulsive stimulated scattering in the Earth and planetary sciences, Annu. Rev. Phys. Chem., 50, Aleksandrov, K. S., Ryzhova, T. V. (1961a) The elastic properties of rock-forming minerals: pyroxenes and amphiboles, Bulletin. USSR Academy of Science, Geophysics, Ser. 9, Aleksandrov, K. S., Ryzhova, T. V. (1961b) Elastic properties of rock-forming minerals II. Layered silicates, Bulletin. USSR Academy of Science, Geophysics, Ser. 9, Angel R. J. (2001) EOS-FIT V5.2 users guide. Program revision August 2008 Audet P., Bostock M. G., Boyarko D. C., Brudzinski M. R. and Allen R. M. (2010) Slab morphology in the Cascadia fore arc and its relation to episodic tremor and slip. J. Geophys. Res., 115, Barberini, V., Burlini, L., Zappone, A. (2007) Elastic properties, fabric and seismic anisotropy of amphibolites and their contribution to the lower crust reflectivity, Tectonophysics, 445, Bezacier, L., Reynard, B., Bass, J. D., Wang, J., Mainprice, D. (2010) Elasticity of glaucophane, seismic velocities and anisotropy of the subducted oceanic crust, Tectonophysics, 494, Brown, J. M. (2015), Determination of Hashin-Shtrikman bounds on the isotropic effective elastic moduli of polycrystals of any symmetry, Comput. Geosci., 80, 95 99, doi: /j.cageo Brown, J.M., (2016) Determination of elastic moduli from measured acoustic velocities, Comput. Geosci., submitted Brown, J. M., Angel, R. J., and Ross, N. L. (2016) Elasticity of plagioclase feldspars, J. Geophys. Res. Solid Earth, 121, doi: /2015jb Brown, J. M., Abramson, E. H., Ross, R. L. (2006) Triclinic elastic constants for low albite, Phys. Chem. Minerals, 33, Chheda, T. D., Mookherjee, M., Mainprice, D., dos Santos, A. M., Molaison, J. J., Chantel, J., Manthilake, G., Bassett, W. A. (2014), Structure and elasticity of phlogopite under compression: Geophysical implications, Phys. Earth Planet. Int., 233, 1-12, doi: /j.pepi Christensen, N. I., and Mooney, W. D. (1995) Seismic velocity structure and composition of the continental crust: A global view, J. Geophys. Res., 100,

15 Christensen, N. I. (1996) Poisson's ratio and crustal seismology, J Geophys. Res., 101, Collins, M. C., and Brown, J. M. (1998) Elasticity of an upper mantle clinopyroxene, Phys. Chem. Min., 26, Comodi, P., Mellini, M., Ungaretti, L., Zanazzi, P.F. (1991) Compressibility and high pressure structure refinement of tremolite, pargasite and glaucophane, Eur. J. Mineral., 3, Hacker, B. R., Abers, G. A. & Peacock, S. M. (2003a). Subduction factory, 1, Theoretical mineralogy, density, seismic wave speeds, and H2O content. J. Geophys. Res., 108, 2029, doi: /2001jb Hacker, B. R., Peacock, S. M., Abers, G. A. and Holloway, S. D. (2003b) Subduction factory, 2, Are intermediate-depth earthquakes in subducting slabs linked to metamorphic dehydration reactions?, J. Geophys. Res., 108, 2030, doi: /2001jb Hawthorn, F.C., Oberti, R. (2007) Amphiboles: Crystal chemistry, Rev. Mineral. & Geochem., 67, Hawthorne, F.C., Oberti, R., Harlow, G.E., Maresch, W. V., Martin, R. F., Schumacher, J. C., Welch, M. D. (2012) Nomenclature of the amphibole supergroup, Am. Mineral., 97, Holland, T. J. B., and Powell, R. (1998) An internally consistent thermodynamic data set for phases of petrological interest, J. Metamorph. Geol., 16, , Isaak, D. G., Ohno, I., Lee, P.C. (2006) The elastic constants of monoclinic singlecrystal chrome-diopside to 1,300 K, Phys. Chem. Miner., 32, DOI /s Jenkins, D. M., Corona, J. C., Bassett, W. A., Mibe, K., Wang, Z. (2010) Compressibility of synthetic glaucophane, Phys. Chem. Minerals, 37, DOI /s y. Ji, S., Shao, T., Michibayashi, K., Long, C., Wang, Q., Kondo, Y., Zhao, W., Wang, H., and Salisbury, M.H. (2013) A new calibration of seismic velocities, anisotropy, fabrics, and elastic moduli of amphibole-rich rocks, J. Geophys. Res.: Solid Earth, 118, , doi: /jgrb.50352, 2013 Kandelin, J., Weidner, D. J. (1988a) Elastic properties of hedenbergite, J. Geophys. Res., 93, Kandelin, J., Weidner, D. J. (1988b) The single crystal properties of jadeite, Phys. Earth Planet. Inter., 50, Leake, B.E., Woolley, A.R., Arps, C. E. S. Birch, W. D., Gilbert, M. C., Grice, J. D., Hawthorne, F. C. Kato, A., Kisch, H. J. Krivovichev, V. G. Linthout, K., Laird, J.

16 Mandarino, J. A., Maresch, W. V., Nickel, E. H., Rock, N. M. S., Schumacher, J. C., Smith, D. C., Stephenson, N. C. N., Ungaretti, L., Whittaker, E. J. W., Youzhi, G., (1997) Nomenclature of amphiboles: Report of the subcommittee on amphiboles of the International Mineralogical Association Commission on New Minerals and Mineral Names, Canadian Mineral., 35, Llana-Funez, S., Brown, D. (2012) Contribution of crystallographic preferred orientation to seismic anisotropy across a surface analog of the continental Moho at Cabo Ortegal, Spain, Geol. Soc. Amer. Bul., 124, Rencher, A. C. (2002) Methods of Multivariable Analysis, John Wiley & Sons, New York. Sang, L., Vanpeteghem, C.B., Sinogeikin, S.V., and Bass, J.D. (2011) The elastic properties of diopside, CaMgSi2O6, Am. Mineral., 96, Schumacher, J.C. (2007) Metamorphic amphiboles: Composition and coexistence, Rev. Min. & Geochem, 67, Selway, K., Ford, H., Kelemen, P. (2015) The seismic mid-lithosphere discontinuity, Earth Planet. Sci. Lett., 414, Seront, B., Mainprice, D., and Christensen, N. I. (1993), A determination of the 3- dimensional seismic properties of anorthosite Comparison between values calculated from the petrofabric and direct laboratory measurements, J. Geophys. Res., 98, , doi: /92jb Tatham, D. J., Lloyd, G. E., Butler, R. W. H., Casey, M. (2008) Amphibole and lower crustal seismic properties, Earth Planet. Sci. Lett., 267, Tindle, A.G., Webb, P.C. (1994) Probe-AMPH A spreadsheet program to classify microprobe-derived amphibole analyses, Comput. & Geosci., 20, Vaughan, M.T., Guggenheim, S. (1986) Elasticity of muscovite and its relationship to crystal structure. J. Geophys. Res. 91, Waeselmann, N, Brown, J. M., Angel, R, J., Ross, N., Zhao, J., and Kaminsky, W. (2016) The elastic tensor of monoclinic alkali feldspars, Am. Mineral., doi: /am Watt, J. P., Davies, G. F. and O Connell, R. J. (1976) The elastic properties of composite materials, Rev. Geophys. Space Phys., 14, Watt, J. P. and O Connell, R. J. (1980) An experimental investigation of the Hashin- Shtrikman bounds on two-phase aggregate elastic properties, Phys Earth Planet Int., 21,

17 649 Figures Figure 1. Classification and compositions of magnesium calcium amphiboles plus glaucophane (based on Leake et al. 1997). The axis extending to the right gives increasing aluminum in tetrahedral coordination (from 0 for tremo lite to (Al2Si6O22) for tschermakite). Occupancy of the A-site by (Na+K) (from 0 to 1) is shown in the vertical direction. Substitution of Na for Ca in the B-site extends into the figure with full replacement of Ca by Na found in glaucophane. Named stoichiometric endmember compositions are identified. Full solid-solution replacement of magnesium by iron is labeled by adding ferro- to the end-member names (exceptions ferroactinolite is the iron-bearing form of tremolite). Small filled and numbered circles are compositions of the current samples based on the chemistry provided in Table 2. The large gray circle gives the average chemistry for calcium amphiboles reported by Schumacher (2007). Lines projected to the zero of A-site occupation are provided as an aid in visualizing the sample compositions.

18 Na + K in A Na + K in A iv Aluminum Na in B Iron iv Aluminum vi Aluminum iv Aluminum Figure 2. Compositions of the amphibole samples in formula units reported in Table 2. Plotted numbers correspond to the sample numbers. The gray circle is the average of calcium amphiboles reported by Schumacher (2007). The top two panels show front and side projections of the compositions illustrated in Figure 1 (tetrahedral coordinated aluminum versus A-site occupation and sodium in the B- site vs A-site occupation). The lower left panel shows the number of iron atoms per formula unit vs tetrahedral coordinated aluminum. The lower panel on the right shows octahedral-coordinated aluminum versus tetrahedral-coordinated aluminum

19 C C Modulus (GPa) C 22 Modulus (GPa) C 23 C 12 Modulus (GPa) C 66 C C Total Aluminum (atoms/f.u.) C Total Aluminum (atoms/f.u.) Total Aluminum (atoms/f.u.) Modulus (GPa) C 46 C 15 C 25 C 35 Modulus (GPa) Bulk Modulus Shear Modulus Velocity (km/s) Compressional Transverse Total Aluminum (atoms/f.u.) Total Aluminum (atoms/f.u.) Total Aluminum (atoms/f.u.) Figure 3. Elastic moduli and velocities of amphiboles as a function of total aluminum. Filled symbols are current experimental results with error bars shown when larger than the plotted symbol. The different symbol shapes are associated with particular moduli as labeled in each panel. Points with the X symbols are moduli and velocities for glaucophane (Bezacier et al. 2010). Solid lines are regression predictions for increasing aluminum content in an iron-free mineral. Dashed lines (when present) give the predicted ferro-equivalent behavior. Open symbols (when present) give the prediction of moduli sensitive to iron or A-site occupancy. When no open symbol is plotted, the predicted moduli lie on the solid lines at the appropriate aluminum content.

20 X-Z Plane c X-Y Plane b Y-Z Plane c a* a a* b Diopside c b c a* a a* b Tremolite c b c a* a a* b Pargasite c b c a* a a* b Glaucophane Figure 4. Selected inosilicate elastic wave velocities as a function of propagation direction in three orthogonal planes. For each plane normal to a Cartesian axis light circles represent velocities of 2, 4, 6, 8, and 9.5 km/s. The orientations of crystallographic axes are shown. Thick line are velocities based on the elastic moduli and propagation directions. The inner thick lines are transverse wave velocities, the outer thick line gives compressional velocities. Top row: diopside velocities based on Isaak et al. (2006). Second and third rows: calcium amphibole end-member velocities based on the current work. Dashed line in second row are compressional velocity predictions based on the elastic moduli for a hornblende reported by Aleksandrov and Ryzhova (1961a). Bottom row: glaucophane velocities based on Bezacier et al. (2010).

21 c c a* b a Figure 5. Selected inosilicate strain ellipsoids under hydrostatic stress projected on the crystallographic a-c and b-c planes. Red: diopside from Isaak et al. (2006), Black: tremolite from current work, Magenta: pargasite from current work), Blue: glaucophane. Solid line is based on Bezacier et al. (2010) and dashed is from Jenkins et al. (2010).

22 Tables Sample Unit cell volume (A 3 ) Density kg/m 3 Source unknown unknown Gore Mountain NY, collected by B.W. Evans unknown Lake Wenatchee, WA collected by B.W. Evans RRuff.info #60029 R. Downs RRuff.info #60044 R. Downs RRuff.info #60632 R. Downs Unknown Table 1. Amphibole sample information. Unknown samples were obtained as mineral separates from rocks of unknown origin. Unit cell volumes are from x ray analysis, densities are calculated based on unit cell volumes and microprobe determined chemistry. The uncertainty in unit cell volume is 0.3%. The density uncertainty, accounting for chemistry and volume uncertainties, is 0.5%.

23 Sample GL HBL Structural Formulae Si Al iv Al vi Ti Cr Fe Fe Mn Mg Ca Na K F Cl OH* Total Site Occupancy (Ca+Na) (B) Na (B) (Na+K) (A) Mg/(Mg+Fe 2 ) Fe 3 /(Fe 3 +Al vi ) Table 2. Microprobe chemical analysis in formula units based on Probe-AMPH (Tindle and Webb, 1994) plus the chemical analysis of the glaucophane (GL) sample used in Bezacier et al. (2010) and the average calcium amphibole (HBL) as reported by Schumacher (2007). See supplemental table for weight % oxides measured by microprobe analysis.

24 Gl 2 C C C C C C C C C C C C C Table 3. Elastic moduli (in GPa) of amphiboles. The 2 uncertainties include misfits to velocities and uncertainty in sample densities. The column labeled Gl gives re-analyzed moduli and uncertainties for glaucophane based on velocities reported by Bezacier et al (2010). 716